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SACAC Workshop: Observer Design For Dynamic Systems (Pretoria)

October 12 - October 13

 

PROGRAMME

Day 1: Basics of Observers

This day covers the basic concepts of observability and observers.

08:00 – 08:30 Registration + Coffee/Tea
08:30 – 09:00 Introduction Derik le Roux
What is an observer?
How does it fit into a control loop?

  • Example 1: Inverted PendulumBrunton, S. L. and Kutz, J. N. Data Driven Science and Engineering: Machine Learning, Dynamical Systems and Control. Cambridge University Press, 2019
  • Example 2: CSTRHaseltine, E. L. and Rawlings, J. B. Critical evaluation of extended Kalman filtering and moving-horizon estimation. Ind. Eng. Chem. Res., 44:2451-2460, 2005.
  • Example 3: Falling objectJulier, S., Uhlmann, J., and Durrant-Whyte, H. F. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans. Automatic Control, 45(3):477-482, 2000.

The introduction aims to provide an overview of what an observer is, how it fits into a feedback control system, and why they are important.
09:00 – 10:00 Observability Derik le Roux
  • Definition of Observability
  • Linear Systems
    • Tests for observability for linear systems
      • Rank condition
      • Eigenvalue analysis
      • Observability Gramian
        • Model reduction and degree of observability
  • Nonlinear Systems
    • Observability test using Lie derivatives
  • Decomposition

Observability is an important concept for the design of observers. The concept will be described mainly for linear systems, specifically some of the basic tests to evaluate observability. Observability in the context of nonlinear systems will be discussed briefly.
10:00 – 10:15 Coffee/Tea break
10:15 – 12:00 Observers Derik le Roux / Denis Dochain
  • Luenberger Observer and pole placement
  • Linear Quadratic Regulators, Linear Quadratic Observers and Linear Quadratic Gaussian control.

This section presents some of the foundational aspects of observers which is necessary to understand one of the most common observers, the Kalman Observer.
12:00 – 13:00 Lunch
13:00 – 14:30 More Observers Derik le Roux / Denis Dochain
  • Kalman Observer
  • Extended Kalman Observer
  • Other nonlinear observers (Unscented Kalman Observer)

The most well-known observer, the Kalman Observer, will be discussed. Extensions of the observer for nonlinear systems and the tuning of these observers will be discussed.
14:30 – 15:00 Coffee/Tea break
15:00 – 16:30 Simulations Derik le Roux
  • Exercise A: Inverted Pendulum
  • Exercise B: CSTR
  • Exercise C: Falling object

Participants will play with MATLAB/Simulink simulations to better understand the different observers.

 

Day 2: Advanced topics

This day will cover the main topics as from the following articles:

  • Pannocchia, G., Rawlings, J.B. (2003). Disturbance Models for Offset-Free Model-Predictive Control. AIChE Journal, 39(2), 426-437.
  • D. (2003). State and parameter estimation in chemical and biochemical processes: a tutorial. Journal of Process Control, 13, 801-818.
08:00 – 08:30 Coffee/Tea break
08:30 – 10:00 Offset-free MPC using disturbance observers Derik le Roux
  • What is offset-free MPC?
  • How to estimate disturbances and what are the limitations?
  • Simulations

This section considers how Observers can be included in MPC loops to achieve offset-free setpoint tracking for MPC. It involves extending the model to include input/output disturbances, but with specific limitations.
10:00 – 10:15 Coffee/Tea break
10:15 – 12:00 Asymptotic Observers and Reaction Invariants

The underlying idea of asymptotic observers is to take advantage of the structure of the dynamical models of a processes to rewrite part of the model in a form independent of the process kinetics. This structural property of mass and energy balance is closely related to the notion of reaction invariants.

 Denis Dochain
12:00 – 13:00 Lunch
13:00 – 14:30 Decoupled parameter estimation

Improved estimation performance is possible if the state estimation and the parameter estimation are decoupled from each other.

 Denis Dochain
14:30 – 15:00 Coffee/Tea break
15:00 – 16:30 Simulations

  • Example A: CSTR

Participants will use MATLAB/Simulink simulations to better understand the different observer approaches.

 Denis Dochain / Derik le Roux

Details

  • Start: October 12
  • End: October 13
  • Event Category:

Venue

  • University of Pretoria